The 100-lb block is stationary at time t = 0, and then it is subjected to the force P shown. Note that the force is zero for all times beyond t = 15 sec. Determine the velocity v of the block at time t = 15 sec. Also calculate the time t at which the block again comes to rest.
The driver of a car is practicing handling his car under winter conditions in an empty parking lot. Because of the snow, the friction force between the car's tires and the ground is at most equal to 45% of the normal force mg (i. e. μS = 0.45). When the 1700 kg car is going 8 m/s, and the driver tries to execute a tight turn, what is the tightest radius the car's tires can cause the car to execute? r = m.
Two banked curves have the same radius. Curve A is banked at 13.3∘, and curve B is banked at an angle of 15.3∘. A car can travel around curve A without relying on friction at a speed of 14.7 m/s. At what speed can this car travel around curve B without relying on friction? Number Units
In the figure, particle A moves along the line y = 32.0 m with a constant velocity v→ of magnitude 3.16 m/s and directed parallel to the x axis. At the instant particle A passes the y axis, particle B leaves the origin with zero initial speed and constant acceleration a→ of magnitude 0.494 m/s2. What angle θ between a→ and the positive direction of the y axis would result in a collision?
You drop a 1.40 kg book to a friend who stands on the ground at distance D = 12.0 m below. Your friend's outstretched hands are at distance d′ = 1.60 m above the ground (see the figure). (a) What is the speed of the book when it reaches her hands? (b) If we substituted a second book with twice the mass, what would its speed be when it reaches her hands? (c) If, instead, the book were thrown down with initial speed 7.20 m/s, what would be the answer to (a)? (a) Number Units (b) Number Units (c) Number Units
A spacecraft is traveling with a velocity of v0x = 4920 m/s along the +x direction. Two engines are turned on for a time of 749 s. One engine gives the spacecraft an acceleration in the +x direction of ax = 2.58 m/s2, while the other gives it an acceleration in the +y direction of ay = 8.03 m/s2. At the end of the firing, what is a) vx and b) vy? (a) Number Units (b) Number Units
A certain spring is found not to conform to Hooke's law. The force (in newtons) it exerts when stretched a distance x (in meters) is found to have magnitude 46.8x + 38.0x2 in the direction opposing the stretch. (a) Compute the work required to stretch the spring from x = 0.33 m to x = 0.66 m. (b) With one end of the spring fixed, a particle of mass 2.13 kg is attached to the other end of the spring when it is extended by an amount x = 0.66 m. If the particle is then released from rest, what is its speed at the instant the stretch in the spring is x = 0.33 m? (c) Is the force exerted by the spring conservative or nonconservative? (a) Number Units (b) Number Units (c)
Problem 2(30 points): The 5−kg box has a speed of v0 = 20 m/s when H = 3 m. Given the kinetic friction coeficient μk = 0.1 and R = 9 m, determine the normal force the box exerts on the surface when it reaches the location of θ = 30∘. Neglect the size of the box.
In the figure a potential difference of V = 140 V is applied across a capacitor arrangement with capacitances C1 = 11.3 μF, C2 = 6.66 μF, and C3 = 12.3 μF. What are (a) charge q3, (b) potential difference V3, and (c) stored energy U3 for capacitor 3, (d) q1, (e) V1, and (f) U1 for capacitor 1, and (g)q2, (h) V2, and (i) U2 for capacitor 2 (a) Number Units (b) Number Units (c) Number Units (d) Number Units (e) Number Units (f) Number Units (g) Number Units (h) Number Units (i) Number Units
A spherical drop of water carrying a charge of 41 pC has a potential of 550 V at its surface (with V = 0 at infinity). (a) What is the radius of the drop? (b) If two such drops of the same charge and radius combine to form a single spherical drop, what is the potential at the surface of the new drop? (a) Number Units (b) Number Units
A 26.5 kg block is connected to an empty 1.00 kg bucket by a cord running over a frictionless pulley. The coefficient of static friction between the table and the block is 0.485 and the coefficient of kinetic friction between the table and the block is 0.320. Sand is gradually added to the bucket until the system just begins to move. (a) Calculate the mass of sand added to the bucket. kg (b) Calculate the acceleration of the system. m/s2
A student of weight 621 N rides a steadily rotating Ferris wheel (the student sits upright). At the highest point, the magnitude of the normal force F→N on the student from the seat is 552 N. (a) What is the magnitude of F→N at the lowest point? If the wheel's speed is doubled, what is the magnitude FN at the (b) highest and (c) lowest point? (a) Number Units (b) Number Units (c) Number Units
Two forces, F→1 and F→2, act on the 7.00−kg block shown in the drawing. The magnitudes of the forces are F1 = 70.9 N and F2 = 31.6 N. Take the positive direction to be to the right. Find the horizontal acceleration of the block, including sign. Number Units
In the figure a potential difference of V = 100 V is applied across a capacitor arrangement with capacitances C1 = 11.6 μF, C2 = 6.36 μF, and C3 = 15.4 μF. What are (a) charge q3, (b) potential difference V3, and (c) stored energy U3 for capacitor 3, (d) q1, (e) V1, and (f) U1 for capacitor 1, and (g)q2, (h) V2, and (i) U2 for capacitor 2 (a) Number Units (b) Number Units (c) Number Units (d) Number Units (e) Number Units
The person in the figure below weighs 167 lb. Each crutch makes an angle of θ = 26.0∘ with the vertical (as seen from the front). Half of the person's weight is supported by the crutches, the other half by the vertical forces exerted by the ground on his feet. Assuming he is at rest and the force exerted by the ground on the crutches acts along the crutches, determine each of the following. (a) the smallest possible coefficient of friction between crutches and ground (b) the magnitude of the compression force supported by each crutch Ib
A 0.045-kg golf ball is rolling toward the hole with an approximately constant velocity ⟨0.5, 0, 0⟩ m/s. At t = 0.90 s, it hits the edge of the hole. It then travels around the hole ("rimming out") and continues rolling at a nearly constant momentum. It leaves the hole at t = 1.2 s with a speed 0.34 m/s in the direction ⟨0.45, 0.90, 0⟩. A picture of the ball before and after the interaction is shown below. What is the average net force on the golf ball during the time interval that the ball interacts with the hole?
A 27⋅kg block is connected to an empty 1⋅kg bucket by a cord running over a frictionless pulley. The coefficient of static friction between the table and the block is 0.43 and the coefficient of friction between the table and the block is 0.31. (a) Find the acceleration of the system if 5.3⋅kg of sand is put into the bucket. m/s2 (b) Find the acceleration of the system if 6.4⋅kg more sand is added to the bucket. m/s2
Two blocks, M1 and M2, are connected by a massless string that passes over a massless pulley. M1 has a mass of 2.25 kg and is on an incline of angle θ1 = 45.5∘ that has a coefficient of kinetic friction μ1 = 0.205. M2 has a mass of 6.25 kg and is on an incline of angle θ2 = 35.5∘ that has a coefficient of kinetic friction μ2 = 0.105. The figure illustrates the configuration. The two-block system is in motion, with block M2 sliding down the ramp. Find the magnitude a2 of the acceleration of block M2. a2 = m/s2
Two rods are placed in x−y plane as shown in figure. The right rod has a length of 2 m and a uniform positive total charge of 7 μC. It is placed with its nearest end at a distance 0.5 m from the origin and the axis of the rod makes an angle of 60∘ with the y-axis. The left rod has a length of 3 m, and a uniform negative total charge −12 μC. It is placed with its nearest end at a distance 0.4 m from the origin the axis of the rod makes an angle of 60∘ with the y -axis as shown in figure. Calculate the magnitude and direction of the electric field at the origin due to both rods.
A UPS package full of chocolates that weighs 3 kg is on a ramp that is angled at θ = 25∘ to the horizontal. The coefficient of kinetic friction of the ramp is μk = 0.19. If the UPS package starts from rest at height of 8.15 m from base of the ramp, how fast will it be travelling as it slides down to the bottom of the ramp? m/s