In the figure, a 2.7 kg block is accelerated from rest by a compressed spring of spring constant 640 N/m. The block leaves the spring at the spring's relaxed length and then travels over a horizontal floor with a coefficient of kinetic friction μk = 0.298. The frictional force stops the block in distance D = 8.1 m. What are (a) the increase in the thermal energy of the block-floor system, (b) the maximum kinetic energy of the block, and (c) the original compression distance of the spring?
A 2.30−kg block starts from rest at the top of a 30.0∘ incline and slides a distance of 2.10 m down the incline in 1.80 s. (a) Find the magnitude of the acceleration of the block. m/s2 (b) Find the coefficient of kinetic friction between block and plane. (c) Find the friction force acting on the block. magnitude N direction (d) Find the speed of the block after it has slid 2.10 m. m/s
Two blocks, of weights 2.3 N and 6.2 N, are connected by a massless string and slide down a 28∘ inclined plane. The coefficient of kinetic friction between the lighter block and the plane is 0.090 ; that between the heavier block and the plane is 0.23. Assuming that the lighter block leads, find (a) the magnitude of the acceleration of the blocks and (b) the tension in the string.
A 0.2−kg wad of clay is released from rest and drops h = 0.95 m to a concrete floor. The clay does not rebound, and the collision lasts 0.02 s. Determine the time average of the force which the floor exerts on the clay during the impact.
A 640 kg car pulling a 510 kg trailer accelerates forward at a rate of 2.24 m/s2. Assume frictional forces on the trailer are negligible. Ignore air drag. (a) Calculate the net force (in N) on the car. magnitude N direction (b) Calculate the net force (in N) on the trailer. magnitude N direction ---Select- (c) What is the force (in N) exerted by the trailer on the car? magnitude N direction (d) What is the resultant force exerted by the car on the road? (Assume that the forward direction is along the +x-direction to the right and that the +y-direction points upward. Enter the magnitude in N and the direction in degrees measured from the left of the −y-direction.) magnitude N direction ∘ (measured from the left of the −y-direction)
Consider a conical pendulum with a bob of mass m = 86.0 kg on a string of length L = 10.0 m that makes an angle of θ = 8.00∘ with the vertical. (Consider +i^ to be towards the center of the circular path and +ȷ^ to be upward.) (i) (a) Determine the horizontal and vertical components of the force exerted by the string on the pendulum. Nî + Nȷ^ (b) Determine the radial acceleration of the bob. m/s2
A steady beam of alpha particles (q = +2e, mass m = 6.68×10−27 kg) traveling with constant kinetic energy 26 MeV carries a current of 0.27 μA. (a) If the beam is directed perpendicular to a flat surface, how many alpha particles strike the surface in 3.6 s? (b) At any instant, how many alpha particles are there in a given 23 cm length of the beam? (c) Through what potential difference in volts is it necessary to accelerate each alpha particle from rest to bring it to an energy of 26 MeV? (a) Number Units (b) Number Units (c) Number Units
Three resistors are connected in series across a battery. The value of each resistance and its maximum power rating are as follows: 5.7 Ω and 19.0 W, 29.2 Ω and 13.2 W, and 18.0 Ω and 11.2 W. (a) What is the greatest voltage that the battery can have without one of the resistors burning up? (b) How much power does the battery deliver to the circuit in (a)? (a) Number Units (b) Number Units
A particle moves along a circular path over a horizontal xy coordinate system, at constant speed. At time t1 = 3.40 s, it is at point (4.30 m, 6.90 m) with velocity (3.90 m/s)j^ and acceleration in the positive x direction. At time t2 = 10.3 s, it has velocity (−3.90 m/s)i^ and acceleration in the positive y direction. What are the (a)x and (b)y coordinates of the center of the circular path? Assume at both times that the particle is on the same orbit. (a) Number Units (b) Number Units
A hockey goalie is standing on ice. Another player fires a puck (m = 0.170 kg) at the goalie with a velocity of +66.0 m/s. (a) If the goalie catches the puck with his glove in a time of 4.56×10−3 s, what is the magnitude of the average force exerted on the goalie by the puck? (b) Instead of catching the puck, the goalie slaps it with his stick and returns the puck straight back to the player with a velocity of -66.0 m/s. The puck and stick are in contact for a time of 4.56×10−3 s. Now, what is the magnitude of the average force exerted on the goalie by the puck? Verify that your answers to parts (a) and (b) are consistent with the conclusion of Conceptual Example 3. (a) Number Units (b) Number Units
The magnitude of the velocity of a projectile when it is at its maximum height above ground level is 19 m/s. (a) What is the magnitude of the velocity of the projectile 2.0 s before it achieves its maximum height? (b) What is the magnitude of the velocity of the projectile 2.0 s after it achieves its maximum height? If we take x = 0 and y = 0 to be at the point of maximum height and positive x to be in the direction of the velocity there, what are the (c) x coordinate and (d) y coordinate of the projectile 2.0 s before it reaches its maximum height and the (e) x coordinate and (f) y coordinate 2.0 s after it reaches its maximum height? (a) Number Units (b) Number Units (c) Number Units (d) Number Units (e) Number Units (f) Number Units
13.F5 Two identical spheres A and B, each of mass m, are attached to an inextensible inelastic cord of length L and are resting at a distance a from each other on a frictionless horizontal surface. Sphere B is given a velocity v0 in a direction perpendicular to line AB and moves it without friction until it reaches B′ where the cord becomes taut. Draw the impulse-momentum diagram that can be used to determine the magnitude of the velocity of each sphere immediately after the cord has become taut.
Truck suspensions often have "helper springs" that engage at high loads. One such arrangement is a leaf spring with a helper coil spring mounted on the axle, as shown in the figure below. When the main leaf spring is compressed by distance y0, the helper spring engages and then helps to support any additional load. Suppose the leaf spring constant is 5.20×105 N/m, the helper spring constant is 3.40×105 N/m, and y0 = 0.500 m. (a) What is the compression of the leaf spring for a load of 4.90×105 N? m (b) How much work is done in compressing the springs?
A man is driving his car with speed 46.0 mi/h on a horizontal stretch of road. (a) When the road is wet, the coefficient of static friction between the road and the tires is 0.105. Find the minimum stopping distance (in m). m (b) When the road is dry, μs = 0.602. Find the minimum stopping distance (in m). m
Consider the circuit shown in the figure below, where C1 = 6.00 μF, C2 = 7.00 μF, and ΔV = 22.0 V. Capacitor C1 is first charged by closing switch S1. Switch S1 is then opened, and the charged capacitor is connected to the uncharged capacitor by closing S2. (a) Calculate the initial charge acquired by c1. (Round your answer to at least one decimal place.) μC (b) Calculate the final charge on each capacitor. q1 = μC q2 = μC
A 98 g red superball traveling 21 m/s EAST has an elastic collision with a 53 g blue superball traveling 7 m/s EAST. Find the final speeds and directions of the superballs. Also determine how much thermal energy was generated during the collision.
The circuit in the figure below consists of two identical, parallel metal plates connected to identical metal springs, a switch, and a 136-V battery. With the switch open, the plates are uncharged, are separated by a distance d = 7.60 mm, and have a capacitance C = 2.00 μF. When the switch is closed, the distance between the plates decreases by a factor of 0.500. (a) How much charge collects on each plate? μC (b) What is the spring constant for each spring? kN/m
Two metal spheres, each of radius 2.9 cm, have a center-to-center separation of 2.8 m. Sphere 1 has a charge of +1.2×10−8 C; sphere 2 has a charge of −4.0×10−8 C. Assume that the separation is large enough for us to assume that the charge on each sphere is uniformly distributed (the spheres do not affect each other). With V = 0 at infinity, calculate in volts (a) the potential at the point halfway between their centers and the potential on the surface of (b) sphere 1 and (c) sphere 2. (a) Number Units (b) Number Units (c) Number Units
A rectangular loop carries a current of 10 A. It is placed in a uniform magnetic field of 4.27 T. The field is parallel to the horizontal plane. The plane of the loop makes an angle of θ = 13∘ with the horizontal. When viewed from above, the current in the loop is counter-clockwise. The area of the loop is 203 cm2. What is the magnitude of the torque on the loop? Write your answer in the units of newton-meter (N. m) in decimal form with three digits to the right of the decimal point (e. g. 5.327); do not write any units or sign.
a) calculate the acceleration of the body whose mass is 10 kg. By applying a force of 100 N, as shown in the figure. b) Calculate the acceleration of the same body, but considering that the coefficient of dynamic friction between the block and the surface is 0.2.8) On an inclined plane 1.5 m high and 4 m base, there is a body that weighs 100 kgf, what force parallel to the plane must be applied so that the body is in balance and about to decrease the coefficient of friction between the body and the plane is 0.25 10) A block weighing 23 kgf slides on a horizontal surface by a force that pulls the block with an angle of 30 degrees and a magnitude of 220 N if the coefficient of dynamic friction is 0.35. Calculate the acceleration acquired by the block.
A long, straight wire going through the origin is carrying a current of 3.00 A in the positive z-direction (Fig, P19.44). At a point a distance r = 1.20 m from the origin on the positive x-axis, find the a. magnitude and b. direction of the magnetic field. At a point the same distance from the origin on the negative y-axis, find the c. magnitude and d. direction of the magnetic field. Figure P19.44 Details An illustration shows a wire along z axis carrying current I upward. Vector B in xy plane is a circle of radius r.
4. (20 points) Two blocks are tethered together with a rope. Block A has mass 2 kg, Block B has mass 10 kg. A force F = 50 N at an angle Θ = 20 deg is pulling Block B to the right. The tension in the rope is unknown and labeled as T. Assuming the blocks are sliding and on a rough surface with coefficient of kinetic friction μk = 0.4, find the acceleration of the boxes (magnitude and direction) and the magnitude of the tension in the rope. You will need to use Newton's Laws for this problem. Hint: Break the system up and analyze the blocks each with their own FBD/equations. Don't forget the blocks are connected to each other.
A carnival Rotor-ride has radius R = 5.0 m and a frequency of rotation f = 0.50 rev/s. What is the minimum coefficient of static friction μs, that will keep a person of mass m from sliding down when the bottom falls out? Let Ffr = Force of friction A) μs = 0.20 B) μs = 0.51 C) μs = 0.13 D) μs = 0.29 E) μs = 0.46 F) None of these
In the figure, wheel A of radius rA = 9.07 cm is coupled by belt B to wheel C of radius rC = 23.4 cm. The angular speed of wheel A is increased from rest at a constant rate of 1.28 rad/s2. Find the time needed for wheel C to reach an angular speed of 146 rev/min, assuming the belt does not slip. (Hint: If the belt does not slip, the linear speeds at the two rims must be equal.)
The 0.07-kg particle has a speed v = 8.6 m/s as it passes the position shown. The coefficient of kinetic friction between the particle and the vertical-plane track is μk = 0.24. Determine the magnitude of the total force exerted by the track on the particle. What is the change in speed v˙ (positive if speeds up, negative if slows down) of the particle? Answers: F = N v˙ = m/s2
A skateboarder is skating through a half-pipe with a radius of 4 m. Initially she is in a crouched position with her center of mass 0.5 m above the surface of the half-pipe. She starts from rest with her center of mass a height of 3 m above the base of the half-pipe and experiences no loss of energy from friction as she moves. At the bottom of the half-pipe she stands up and lifts her arms into the air, thereby raising her center of mass to 1.0 m. She then continues up the other side of the half-pipe. She had to perform work to lift her arms while skating. How much work (in J) did she do if her mass is 78 kg? You may model the skateboarder as a point particle.
A skateboarder with his board can be modeled as a particle of mass 72.0 kg, located at his center of mass. As shown in the figure below, the skateboarder starts from rest in a crouching position at one lip of a half-pipe (point A). On his descent, the skateboarder moves without friction so that his center of mass moves through one quarter of a circle of radius 5.70 m. (a) Find his speed at the bottom of the half-pipe (point (B). m/s (b) Immediately after passing point B, he stands up and raises his arms, lifting his center of mass and essentially "pumping" energy into the system. Next, the skateboarder glides upward with his center of mass moving in a quarter circle of radius 5.32 m, reaching point (D). As he passes through point (D), the speed of the skateboarder is 4.73 m/s. How much chemical potential energy in the body of the skateboarder was converted to mechanical energy when he stood up at point (B) J (c) How high above point (D) does he rise? m
A horizontal, parallel-sided plate of glass having a refractive index of 1.47 is in contact with the surface of water in a tank. A ray coming from above in air makes an angle of incidence of 38.0∘ with the normal to the top surface of the glass. Part A What angle does the ray refracted into the water make with the normal to the surface? Use 1.33 for the index of refraction of water. Express your answer in radians. θ = radians