The 3 kg block is released from rest at A and slides down the smooth parabolic surface (y = x2). Determine the maximum compression of the spring. (Ans. s = 0.243 m)
Figure (a) shows a red car and a green car that move toward each other. Figure (b) is a graph of their motion, showing the positions xg0 = 250 m and xr0 = −35 m at time t = 0. The green car has a constant speed of 22 m/s and the red car begins from rest. What is the acceleration magnitude of the red car? (a) (b) Number Units m/s
A person pushes a 22.6 kg shopping cart at a constant velocity for a distance of 28.7 m on a flat horizontal surface. She pushes in a direction 20.1∘ below the horizontal. A 53.3-N frictional force opposes the motion of the cart. (a) What is the magnitude of the force that the shopper exerts? Determine the work done by (b) the pushing force, (c) the frictional force, and (d) the gravitational force. (a) Number Units (b) Number Units (c) Number Units (d) Number Units
A mass of 0.4 kg hangs motionless from a vertical spring whose length is 1.09 m and whose unstretched length is 0.64 m. Next the mass is pulled down to where the spring has a length of 1.33 m and given an initial speed upwards of 1.2 m/s. What is the maximum length of the spring during the motion that follows? maximum length = m
Part A The 150-lb man lies against the cushion for which the coefficient of static friction is μs = 0.5. (Figure 1) Figure 1 of 1 Determine the resultant normal and frictional forces the cushion exerts on him if, due to rotation about the z axis, he has a constant speed v = 21 ft/s. Neglect the size of the man. Take θ = 60∘. Enter the normal and frictional forces separated by a comma. Express your answers using three significant figures.
An m = 15.0−kg mass is held at rest on a frictionless table against a compressed spring with spring constant k = 4030 N/m. When the mass is released, the spring accelerates it to speed v = 3.05 m/s. There is a rough patch of surface to the right of the spring. The coefficient of friction of this rough patch is μk = 0.430
In the figure, a solid 0.1 kg ball rolls smoothly from rest(starting at height H = 5.9 m) until lit leaves the horizontal section at the end of the track, at height h = 2.2 m. How far horizontally from point A does the ball hit the floor? Number Units
The figure shows an overhead view of a 0.0210 kg lemon half and two of the three horizontal forces that act on it as it is on a frictionless table. Force F→1 has a magnitude of 3.00 N and is at θ1 = 27.0∘. Force F→2 has a magnitude of 6.00 N and is at θ2 = 31.0∘. In unit-vector notation, what is the third force if the lemon half (a) is stationary, (b) has the constant velocity v→ = (12.0i^ − 13.0j^) m/s, and (c) has the varying velocity v→ = (11.0ti^ − 12.0tj^) m/s, where t is time?
Only two forces act on an object (mass = 1.68 kg), as in the drawing. Find (a) the magnitude and (b) the direction (relative to the x axis) of the acceleration of the object. (a) Number Units (b) Number Units
The drawing shows six point charges arranged in a rectangle. The value of q is 7.90 μC, and the distance d is 0.177 m. Find the total electric potential at location P, which is at the center of the rectangle. Number Units
A mass on a spring vibrates horizontally on a smooth, level surface as shown in the figure. Its equation of motion is x(t) = 10 sin(t), where t is in seconds and x is in centimeters. (a) Find the velocity and acceleration at time t. (b) Find the position, velocity, and acceleration of the mass at time t = π/3. In what direction is the mass moving at that time?
Two forces act on a 2.2−kg block resting on a frictionless surface as shown. What is the magnitude of the normal force acting on the block, in newtons?
A 13.0 kg stone slides down a snow-covered hill (Figure 1), leaving point A at a speed of 12.0 m/s. There is no friction on the hill between points A and B, but there is friction on the level ground at the bottom of the hill, between B and the wall. After entering the rough horizontal region, the stone travels 100 m and then runs into a very long, light spring with force constant 2.10 N/m. The coefficients of kinetic and static friction between the stone and the horizontal ground are 0.20 and 0.80 , respectively. Figure 1 of 1 Part A What is the speed of the stone when it reaches point B? Express your answer in meters per second to three significant figures. v2 = m/s Submit Request Answer Part B How far will the stone compress the spring? Express your answer in meters to three significant figures. x = Submit Request Answer Part C Will the stone move again after it has been stopped by the spring? yes no
A 196-kg crate is being pushed across a horizontal floor by a force P that makes an angle of 19.6∘ below the horizontal. The coefficient of kinetic friction is 0.235. What should be the magnitude of P, so that the net work done by it and the kinetic frictional force is zero? Number Units
A spring with a natural height of 57 cm is compressed by a 300 kg mass to a new height of 51 cm. A. What is the spring constant? B. What is the displacement of the spring if the 300 g mass were replaced by a 400 g mass?
A 15.0-kg stone slides down a snow-covered hill (Fig. below), leaving point A with a speed of 10.0 m/s. There is no friction on the hill between points A and B, but there is friction on the level ground at the bottom of the hill, between B and the wall. After entering the rough horizontal region, the stone travels 100 m and then runs into a very long, light spring with force constant 2.00 N/m. The coefficient of kinetic friction between the stone and the horizontal ground is 0.20. (a) What is the speed of the stone when it reaches point B? (15) (b) How far will the stone compress the spring? (15)
A block with a mass of 3.00 kg starts from rest at the top of a 34.5∘ incline and slides 2.00 m down the incline in 1.75 s. (a) What is the magnitude of the acceleration of the block (in m/s2)? m/s2 (b) What is the frictional force (in N ) acting on the block? (Enter the magnitude.) N (c) What is the coefficient of kinetic friction between the block and the incline? (d) What is the speed of the block (in m/s ) after it has slid 2.00 m? m/s
m = 2.7 kg k = 398 N/m δ = 38 mm θ = 25∘ Find the amount which the spring is compressed after the mass comes to rest. Assume a kinetic coefficient of friction of 0.13 and an initial velocity along the surface of v = 2 m/s. Answer:
As in the figure, a mass is attached to two springs (one on either side). The two spring constants are different: k1 = 1480 N/m and k2 = 1990 N/m. If mass m is moved 2.8 cm away from the equilibrium position (where the net force acting on the mass is zero), what will be the magnitude of the net spring force acting on the mass be? N If the net spring force acting on the mass is known to be 63 N (directed to the right), what is the displacement of the mass away from its equilibrium position (use a negative sign for a displacement to the left and positive for a displacement to the right): cm
Throcky skateboards down a frictionless circular ramp. He moves through a quarter circle with radius R = 3.00 m. Throcky and his skateboard have a total mass of m = 25.0 kg, (a) Find his speed at the bottom of the ramp. (b) Find the normal force that acts on him at the bottom of the curve. (c) Suppose that the ramp is not frictionless, and that Throcky's speed at the bottom is only 6.00 m/s, not the 7.67 m/s we found there. What work was done on him by the friction force? (a) At point (1) (b)
Two forces are applied on a 2.00 kg box to move it. In the overhead view of the system, one force has a magnitude of 20.0 N and is applied along the +x axis. This results in an acceleration of the box of magnitude 12.0 m/s2 in the direction given by the angle θ = 30∘ as shown in the diagram below. (a) Determine the magnitude of the second force. (b) Determine the direction of the second force. After a while, a third force is applied on the box and as a result it now moves with a constant velocity. (c) What is the magnitude of the third force? (d) What is the direction of the third force? (e) Draw all three forces in the overhead view of the box.
The two bodies have the masses and initial velocities shown in the figure. The coefficient of restitution for the collision is e = 0.37, and friction is negligible. If the time duration of the collision is 0.029 s, determine the magnitude of the average impact force which is exerted on the 4.6−kg body. Answer: Fave = N
The gold block is mass m1 with a coefficient of kiinetic friction of μk. The blue block is mass m2 and is accelerating downwards. m1 and m2 are connected by a light string that does not slip on the pulley of mass M and radius R. T1 acts on m1 and T2 acts on m2. Choose the correct answer comparing the magnitudes of T1 and T2. T1 = T2 T1 > T2 T1 < T2
You and your bicycle have combined mass 80.0 kg. When you reach the base of a bridge, you are traveling along the road at 5.00 m/s (Figure 1). At the top of the bridge, you have climbed a vertical distance of 5.20 m and have slowed to 2.50 m/s. You can ignore work done by friction and any inefficiency in the bike or your legs. Figure 1 of 1 Part A What is the total work done on you and your bicycle when you go from the base to the top of the bridge? Express your answer in joules. Submit Request Answer Part B How much work have you done with the force you apply to the pedals? Express your answer in joules. W = J
A person is riding a bicycle, and its wheels have an angular velocity of 12.2 rad/s. Then, the brakes are applied and the bike is brought to a uniform stop. During braking, the angular displacement of each wheel is 16.9 revolutions. (a) How much time does it take for the bike to come to rest? (b) What is the angular acceleration (in rad/s2) of each wheel? (a) Number Units (b) Number Units
A ball of radius 0.200 m rolls with a constant linear speed of 2.68 m/s along a horizontal table. The ball rolls off the edge and falls a vertical distance of 2.10 m before hitting the floor. What is the angular displacement of the ball while the ball is in the air? θ =
A star has a mass of 1.74×1030 kg and is moving in a circular orbit about the center of its galaxy. The radius of the orbit is 4.0×104 light-years (1 light-year = 9.5×1015 m), and the angular speed of the star is 2.5×10−15 rad/s. (a) Determine the tangential speed of the star. (b) What is the magnitude of the net force that acts on the star to keep it moving around the center of the galaxy? (a) Number Units (b) Number Units
A person is riding a bicycle, and its wheels have an angular velocity of 15.6 rad/s. Then, the brakes are applied and the bike is brought to a uniform stop. During braking, the angular displacement of each wheel is 14.7 revolutions. (a) How much time does it take for the bike to come to rest? (b) What is the angular acceleration (in rad/s2) of each wheel? (a) Number Units (b) Number Units
A bicycle is rolling down a circular portion of a path; this portion of the path has a radius of 7.75 m. As the drawing illustrates, the angular displacement of the bicycle is 0.973 rad. What is the angle (in radians) through which each bicycle wheel (radius = 0.310 m) rotates? Number Units
The leg and cast in the figure below weigh 238 N(w1). Determine the weight w2 and the angle a needed so that no force is exerted on the hip joint by the leg plus cast. w2 = N a = ∘
You are riding a bicycle along a level road. Assume each wheel is 28 inches in diameter, the rear sprocket has a radius of 3 inches, and the front sprocket has a radius of 7 inches. How fast do you need to pedal (in revolutions per minute) to achieve a speed of 20 mph? (Round your answer to the nearest whole number.) rpm
A bicycle is rolling down a circular portion of a path; this portion of the path has a radius of 9.19 m. As the drawing illustrates, the angular displacement of the bicycle is θ = 0.964 rad. What is the angle (in radians) through which each bicycle wheel (radius = 0.450 m) rotates? rad
A bicycle and rider, with a combined mass of 90 kg, are decelerating at 3 m/s2 on a horizontal surface. The rear contact point is 0.4 m behind the center of gravity. The front contact point is 0.6 m in front of the center of gravity. And, the center of gravity is 1.2 m above the ground. What are the normal forces NF and NR that the ground is putting on the wheels of the bicycle?
Determine the slowest speed that the 74 kg bike racer can travel around a curved track with a 65 m radius without slipping. The track is banked at 61 degrees. Assume the static coefficient of friction is μs = 0.3 and the kinetic coefficient of friction is μk = .2. Also assume the biker will slip before they tip over. Give your answer rounded to 1 decimal place. Number Units
A bicyclist rides down the road on a bike with wheels that have a diameter of 28 in. She is bicycling at 16 miles per hour. ( 5280 feet = 1 mile.) a) What is the angular speed of the wheel in radians per minute? Give an exact answer (no decimals). rad/min b) What is the angular speed in revolutions per minute? Give an exact answer in terms of π. rpm c) What is the approximate angular speed in revolutions per minute? (rounded to two decimal places)? rpm
You're riding your 19 kg bike at a steady 26 km/hr when you experience a steady 25 N force from a headwind. Calculate the power you must supply to maintain a steady speed if your mass is 62 kg. Please report this power in Watts to 0 Work, energy and power decimal places.
Suppose you are riding a stationary exercise bicycle, and the electronic meter indicates that the wheel is rotating at 14.6 rad/s. The wheel has a radius of 0.443 m. If you ride the bike for 42.7 min, how far would you have gone if the bike could move? Number Units
The tires of a bicycle have radius 12.0 in. and are turning at the rate of 205 revolutions per min. See the figure. How fast is the bicycle traveling in miles per hour? (Hint: 5280 ft = 1 mi) How fast is the bicycle traveling? mph (Type an integer or decimal rounded to the nearest tenth as needed.)
As shown in the picture, a man is biking from the top to the bottom of a hill. At the top of the hill, his speed is 1 m/s. When he reaches the foot of the hill, his speed increased to 10 m/s. During this process, 1500 J heat was produced by the man and dissipated to the environment. The height of the hill is 50 m. The weight of the man and his bike is 80 kg. Please compute the work done by the cyclist (W) and the internal energy change (ΔU).
A person is riding a bicycle, and its wheels have an angular velocity of 29.9 rad/s. Then, the brakes are applied and the bike is brought to a uniform stop. During braking, the linear displacement of each wheel is 9.1 m. What is the magnitude angular acceleration (in rad /s2) of each wheel, if the radius of each wheel is 0.6 m ? Answer to 3 sig figs.
A person who weighs 624 N is riding a 91−N mountain bike. Suppose the entire weight of the rider plus bike is supported equally by the two tires. If the gauge pressure in each tire is 7.10×105 Pa, what is the area of contact between each tire and the ground?
A hoop of mass M = 4 kg and radius R = 0.4 m rolls without slipping down a hill, as shown in the figure. The lack of slipping means that when the center of mass of the hoop has speed v, the tangential speed of the hoop relative to the center of mass is also equal to vCM, since in that case the instantaneous speed is zero for the part of the hoop that is in contact with the ground (v − v = 0). Therefore, the angular speed of the rotating hoop is ω = vCM/R. (a) The initial speed of the hoop is vi = 2 m/s, and the hill has a height h = 4.0 m. What is the speed vf at the bottom of the hill? vf = m/s (b) Replace the hoop with a bicycle wheel whose rim has mass M = 4 kg and radius R = 0.4 m, and whose hub has mass m = 1.8 kg, as shown in the figure. The spokes have negligible mass. What would the bicycle wheel's speed be at the bottom of the hill? (Assume that the wheel has the same initial speed and start at the same height as the hoop in part (a)). vf = m/s
You are trying to raise a bicycle wheel of mass m and radius R up over a curb of height h. To do this, you apply a horizontal force F→, as shown in the figure. Feel free to assume that h < R, as shown in the picture. (a) What is the smallest magnitude of the force F→ that will succeed in raising the wheel onto the curb when the force is applied at the center of the wheel? (b) What if the force is applied at the top of the wheel? (c) In which case is less force required?
The leg and cast in the figure below weigh 186 N(w1). Determine the weight w2 and the angle α needed so that no force is exerted on the hip joint by the leg plus cast. w2 = N α =
Suppose you are riding a stationary exercise bicycle, and the electronic meter indicates that the wheel is rotating at 12.6 rad/s. The wheel has a radius of 0.486 m. If you ride the bike for 31.1 min, how far would you have gone if the bike could move? Number Units
Consider the cyclist shown in the figure. The combined center of mass of him and his bicycle is marked as CM, it is a height h above the road, and equally distanced from both wheels by length L. The total mass here is M. The cyclist is riding with velocity v when he must make a sudden stop by hitting brakes on both wheels. a) What are the normal and friction forces that the road exerts on the front and the back wheel if the coefficient of kinetic friction between the road and the wheels is μk? b) What should the ratio of h and L be so that the bicycle will not overturn and throw the cyclist over the handles?
A bicycle is rolling down a circular portion of a path; this portion of the path has a radius of 8.80 m. As the drawing illustrates, the angular displacement of the bicycle is 0.874 rad. What is the angle (in radians) through which each bicycle wheel (radius = 0.360 m) rotates? Number Units
25.21.E. A mountain biker is in a gear where the rear ring has radius 12 cm and the front ring has radius 5.0 cm. If the wheels have radius 0.37 m, then what rate must he pedal in revolutions per second so that the bike moves up the hill at 3 mph (i.e., 1.34 ms)? ANS: 1.4
Two blocks, A and B, are arranged as indicated in the sketch. Each have a mass of 3 kg. The 40∘ incline is frictionless. The 20∘ incline has a coefficient of kinetic friction of 0, 1 . The objects accelerate in the direction indicated on the sketch. 4.1. State Newton's Second Law of Motion in words. 4.2. Draw a free body diagram for the block labelled B. 4.3. Define normal force. 4.4. Calculate the magnitude of the frictional force acting on block B. 4.5. Calculate the magnitude of the acceleration of block A. 4.6. Calculate the magnitude of the tension in the cable. 4.7. The angle of the incline of block A is decreased steadily to 30∘. What effect does this have on the magnitude of the acceleration of the system? Explain using relevant formulae. No calculations needed.