You go down a water slide of length \(L\) that makes an angle \(\theta\) with the horizontal, starting from rest. Do not neglect friction (use \(\mu_k\) as the coefficient of kinetic friction). Determine your acceleration.
What force must be applied to a \(100 ~\mathrm{kg}\) crate on a frictionless plane inclined at \(30°\) to cause an acceleration of \(2 ~\mathrm{m/s^2}\) up the plane?
Shown below is a \(30 ~\mathrm{kg}\) block resting on a frictionless ramp inclined at \(60°\) to the horizontal. The block is held by a spring that is stretched \(5 ~\mathrm{cm}\text{.}\)
Find the tension in the rope and the force that the mountain climber must exert with her feet on the vertical rock face to remain stationary. Assume that the force is exerted parallel to her legs. Also, assume negligible force exerted by her arms.
The force of gravity on an 80-kg person is about \(800 \mathrm{~N}\text{.}\) Suppose this person is standing on a scale in an elevator that is moving upwards but slowing down with an acceleration magnitude of \(1 \mathrm{~m/s^2}\text{.}\) What value does the scale read?
An 80-kg person stands at rest on a scale while pulling vertically downward on a rope that is hanging at rest directly above them. Use \(g = 9.80 \mathrm{~m/s^2}\text{.}\) With what force magnitude must the rope’s tension be pulling on the person so that the scale reads \(500 \mathrm{~N}\text{?}\) With what force magnitude must the rope’s tension be pulling on the person so that the scale reads 25% of the person’s weight? What is the critical magnitude of tension in the rope so that the person just begins to lift off the scale?
On a windy day, a 1.50-kg ball is dropped from rest from a height of 19.6 meters above the Earth’s surface. A steady wind pushes on the falling ball with a constant, horizontal force of 8.40 N, to the right. What is the total displacement of the ball from its initial location to its point of impact on the ground? Use a standard coordinate system with the origin located at the ball’s initial location. Also, use \(g = 9.80 \mathrm{~m/s^2}\text{.}\) Assume no air effects other than the steady wind.
In which of the following situations is the friction force that is acting on the object not in the opposite direction of the object’s velocity? Choose all that apply.
A block, initially at rest in the bed of a stationary pick-up truck, begins to slide to the back of the truck as the truck accelerates and moves forwards.
A block initially at rest in the bed of a stationary pick-up truck does not slide but begins to move forwards with the truck as the truck accelerates and moves forwards.
A \(1.40 \mathrm{~kg}\) block is at rest on a level table. The coefficient of static friction between the table and the block is 0.40, and the coefficient of kinetic friction between the two is 0.10. A person then applies a \(6.00 \mathrm{~N}\) force at an angle of \(30^o\) downward relative to the positive \(x\)-direction. Use \(g = 9.80 \mathrm{~m/s^2}\) and a standard coordinate system. What is the magnitude of the friction force acting between the block and table? What is the acceleration of the block? What is the acceleration of the block if the person applies the \(6.00 \mathrm{~N}\) force at an angle of \(30.0^o\) upward relative to the positive-x direction?
