Calculation 4.10.1. Rope Climbing Tension.
Suppose Kevin, a \(60 ~\mathrm{kg}\) gymnast, climbs a rope.
Section 4.10 Practice - Forces
Subsection Practice
Calculation 4.10.2. Block up a Ramp I.
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?
Calculation 4.10.3. Block up a Ramp II.
A \(2 ~\mathrm{kg}\) block is on a perfectly smooth ramp that makes an angle of \(30°\) with the horizontal.
(a)
What is the block’s acceleration down the ramp and the force of the ramp on the block?
Answer.
\(4.9 ~\mathrm{m/s^2}\text{;}\) \(17 ~\mathrm{N}\)
(b)
What force applied upward along and parallel to the ramp would allow the block to move with constant velocity?
Answer.
\(9.8 ~\mathrm{N}\)
Calculation 4.10.4. The Block, the Spring, and the Ramp.
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 \(5 ~\mathrm{cm}\text{.}\)
What is the spring constant of the spring?
Calculation 4.10.5. Block up a Ramp III.
A force is applied to a block to move it up a \(30°\) incline. The incline is frictionless; \(F = 60 ~\mathrm{N}\) and \(M = 5 ~\mathrm{kg}\text{,}\)
(a)
What is the magnitude of the acceleration of the block?
Calculation 4.10.6. Mountain Climber.
Consider the \(52 ~\mathrm{kg}\) mountain climber shown below.
(a)
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.
Answer.
\(272 ~\mathrm{N}\text{;}\) \(512 ~\mathrm{N}\)
(b)
What is the minimum coefficient of friction between her shoes and the cliff?
Answer.
0.268
Calculation 4.10.7. Corner Hanging Mass.
As shown below, if \(M = 5.5 ~\mathrm{kg}\text{,}\)
(a)
What is the tension in string 1?
Answer.
\(199 ~\mathrm{N}\)
Subsection Additional Practice
Calculation 4.10.8. Elevator.
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?
Answer.
720 N
Calculation 4.10.9. Pulling on a rope.
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?
Calculation 4.10.10. Dropping a ball.
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.
Answer.
\(\Delta \vec{r} = 11.2 \mathrm{m} \hat{x} - 19.6 \mathrm{m} \hat{y}\)
Calculation 4.10.11. Direction of friction.
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 slides to rest on a stationary table.
- 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 car initially at rest does a burnout. (It begins to accelerate and move forward as the wheels spin on the ground.)
Answer.
(B), (C), (D)
Calculation 4.10.12. Pushing on a block.
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?
References References
[1]
Practice activities adapted from OpenStax: https://openstax.org/books/university-physics-volume-1/pages/5-problems.
[2]
Additional practice activities provided by BoxSand: https://boxsand.physics.oregonstate.edu/welcome.
