An 1800 kg block moves on a smooth plane, as shown in Figure 2, towards a "nested" spring assembly. The outer spring A has a stiffness of 5000 N/m, and the inner spring B has a stiffness of 10000 N/m. a) Calculate the maximum compression for each spring. b) If the plane has a kinetic friction coefficient of 0.25, determine the distance from the wall where the block will come to rest after rebounding. Figure 2
A block of mass of 4 kg starts at rest. It is then is pushed by a force of F = 100 N at an angle of θ = 10∘ to the horizontal. The coefficient of kinetic friction between the block and the ground is μk = 0.4. What is the power of force F at time t = 3 s? P = W
The 90.0−lb boy at A is suspended from the cable that passes over the quarter circular cliff rock as shown in (Figure 1). Determine if it is possible for the 175-lb woman to hoist him up. The coefficient of static friction between the cable and the rock is μs = 0.2, and between the shoes of the woman and the ground μs′ = 0.8. Determine the tension in the portion of the cable that the woman is holding. Express your answer to three significant figures and include the appropriate units. Determine the maximum possible force due to friction that opposes the motion of the woman. Express your answer to three significant figures and include the appropriate units.
A 12 N horizontal force F→ pushes a block weighing 5.0 N against a vertical wall (see the figure). The coefficient of static friction between the wall and the block is 0.68 , and the coefficient of kinetic friction is 0.37 . Assume that the block is not moving initially. (a) Will the block move? ("yes" or "no") (b) In unit-vector notation Fxi^ + Fyj^, what is the force on the block from the wall? (a) (b) Number i^ + j^ Units
Three astronauts, propelled by jet backpacks, push and guide a 144 kg asteroid toward a processing dock, exerting the forces shown in the figure, with F1 = 32.0 N, F2 = 56.0 N, F3 = 45.0 N, θ1 = 30.0∘, and θ3 = 60.0∘. What is the (a) magnitude and (b) angle (measured relative to the positive direction of the x-axis in the range of (−180∘, 180∘) of the asteroid's acceleration? (a) Number Units (b) Number Units
To push a 26.0 kg crate up a frictionless incline, angled at 25.0∘ to the horizontal, a worker exerts a force of 219 N parallel to the incline. As the crate slides 1.7 m, how much work is done on the crate by (a) the worker's applied force, (b) the gravitational force on the crate, and (c) the normal force exerted by the incline on the crate? (d) What is the total work done on the crate? (a) Number Units (b) Number Units (c) Number Units (d) Number Units
A farmer's tractor, travelling at 3 m/s, pulls a rope of fixed length attached to a bale of hay through a pulley. Using the dimensions indicated in the picture below how fast is the bale rising when x = 5 m ?
A 218-kg log is pulled up a ramp by means of a rope that is parallel to the surface of the ramp. The ramp is inclined at 29.5∘ with respect to the horizontal. The coefficient of kinetic friction between the log and the ramp is 0.844 , and the log has an acceleration of 0.746 m/s2. Find the tension in the rope. Number Units
A yo-yo has a rotational inertia of 766 g⋅cm2 and a mass of 116 g. Its axle radius is 2.94 mm, and its string is 143 cm long. The yo-yo rolls from rest down to the end of the string. (a) What is the magnitude of its linear acceleration? (b) How long does it take to reach the end of the string? As it reaches the end of the string, what are its (c) linear speed, (d) translational kinetic energy, (e) rotational kinetic energy, and (f) angular speed? (a) Number Units (b) Number Units (c) Number Units (d) Number Units (e) Number Units (f) Number Units
A person drags a 30 kg box across the floor by pulling on a rope at an angle of 20∘ above the horizontal. a. Draw a system schema for this scenario. (Model the person and rope as a single object, and model the Earth and floor as a single object.) b. Your system schema above might show a single contact interaction between the floor and the box. However, if the floor is a rough surface, we will split this interaction into two different forces on our free body diagram: a force that is perpendicular to the surface and a force that is parallel to the surface. (We do this because these forces are due to different sorts of physical phenomena and we model them differently, as we will see later in the semester.) Draw a free body diagram for the box with the coordinate system on the right. Label all the forces like F→A on B c. Make a table of the x and y components of all the forces. d. Use your table to write a Newton's second law equation for the sum of the forces in both x and y directions. Do we know either the x component or the y component of the acceleration? If so, what is it? e. Suppose the force of gravity on the box is 300 N, the horizontal contact force is 120 N, and the force of the person pulling on the box is 160 N. Use this with your equations to determine any unknown forces and components of the acceleration. f. Assuming the acceleration you calculated is constant, how much time does it take for the person to pull the box a distance of 10 m if the box starts from rest?
A child on a sled is released on a frictionless, inclined hill of angle θ with respect to the horizontal as shown below. The length of the incline is d. In terms of d, g, and θ, how long does it take the sled and rider to reach the bottom of the hill?
Two people are pulling on opposite sides of a 10 kg box which sits on a floor with no friction. Use g = 10 N/kg if you need to use g. Pulling with 25 N of force Pulling with 40 N of force The magnitude of the box's acceleration is If the box is initially at rest, the speed after 5 seconds of pulling will be
A rope is used to pull a 5.33 kg block at constant speed 2.05 m along a horizontal floor. The force on the block from the rope is 4.17 N and directed 12.9∘ above the horizontal. What are (a) the work done by the rope's force, (b) the increase in thermal energy of the block-floor system, and (c) the coefficient of kinetic friction between the block and floor? (a) Number Units (b) Number Units (c) Number Units
A 222−kg log is pulled up a ramp by means of a rope that is parallel to the surface of the ramp. The ramp is inclined at 27.8∘ with respect to the horizontal. The coefficient of kinetic friction between the log and the ramp is 0.830 , and the log has an acceleration of 0.853 m/s2. Find the tension in the rope. Number Units
To push a 27.0 kg crate up a frictionless incline, angled at 25.0∘ to the horizontal, a worker exerts a force of 219 N parallel to the incline As the crate slides 1.5 m, how much work is done on the crate by (a) the worker's applied force, (b) the gravitational force on the crate, and (c) the normal force exerted by the incline on the crate? (d) What is the total work done on the crate? (a) Number Units (b) Number Units (c) Number Units (d) Number Units
Three astronauts, propelled by jet backpacks, push and guide a 121 kg asteroid toward a processing dock, exerting the forces shown in the figure, with F1 = 35 N, F2 = 55 N, F3 = 38 N, θ1 = 30∘, and θ3 = 60∘. What is the (a) magnitude and (b) angle (measured relative to the positive direction of the x axis in the range of (−180∘, 180∘]) of the asteroid's acceleration? (a) Number Units (b) Number Units
A mountain climber, in the process of crossing between two cliffs by a rope, pauses to rest. She weighs 520 N. As the drawing shows, she is closer to the left cliff than to the right cliff, with the result that the tensions in the left and right sides of the rope are not the same. Find the tensions in the rope to the left and to the right of the mountain climber. TL = TR =
A 30 kg child wants to slide down the slide, which is inclined at an angle of 37∘ above the horizontal. In an effort to make the ride more thrilling, the evil babysitter pulls on the child with a rope along the ramp which exerts a 10 N force as shown in the diagram. What is the magnitude of the normal force acting on the child? (round your value to the nearest hundredths place)
a) Compare the accelerations of: 1) a 2 kg cart with small wheels (negligible moment of inertia) 2) hollow cylinder of mass m2 = 1.5 kg, I = mR2, and 3) a solid ball of mass m3 = 2.5 kg (I = 2 /5 mR2), rolling down a 10 degree incline without slipping. Find the acceleration of the cart, then give a ratio or factor for the accelerations of the other two in terms of the cart's acceleration. b) If the ball and cylinder have the same radius, which one must have more torque exerted on it by static friction while rolling down? c) If we start the ball and hoop from rest at the top of the incline and let them roll for the same amount of time, which will have more angular momentum? (Again assume the radii are the same)