Concept explainers
(a)
To Calculate: The minimum distance to make the car stop.
(a)
Answer to Problem 48P
The minimum distance it takes to stop the car is
Explanation of Solution
Given Information:
An automobile is going up a
The coefficient of static friction between the tires and the road is
Formula Used:
Third equation of motion:
Where symbols have their usual meanings.
Calculation:
Initial velocity of the automobile
Final velocity of the automobile
Let the minimum displacement be
Let the acceleration of the car be
Free body diagram for automobile going up the inclined plane is shown below
Use the third kinematics relation
From the free body diagram, along the x-axis
Along the y-axis:
Substitute
Substitute the value of acceleration in
Conclusion:
Thus, the minimum stopping distance is
(b)
To Calculate: The minimum distance it would take to stop if the car were going down the grade.
(b)
Answer to Problem 48P
Explanation of Solution
Given Information:
An automobile is going up a
The coefficient of static friction between the tires and the road is
FormulaUsed:
Third equation of motion:
Where, symbols have their usual meanings
Calculation:
Initial velocity of the car
Final velocity of the car
Let the minimum displacement be
And let the acceleration of the car be
Use the third kinematic equation
Along the x-axis
And along the y-axis we conclude that,
Substitute
Substitute the value of acceleration in
Here, the negative sign indicates that the displacement of the car is in the opposite direction as in part
Conclusion:
Therefore, the magnitude of displacement is
Want to see more full solutions like this?
Chapter 5 Solutions
PHYSICS F/SCI.+ENGRS.,STAND.-W/ACCESS
- A motorcyclist is coasting with the engine off at a steady speed of 20.0 m/s but enters a sandy stretch where the coefficient of kinetic friction is 0.70. Will the cyclist emerge from the sandy stretch without having to start the engine ifthe sand lasts for 15 m? If so, what will be the speed upon emerging?arrow_forwardYou want to run up a hill starting from standstill. The hill is at an angle of 30 degrees with respect to hortizontal and has a coefficient of static friction of 0.3. How long will it take to reach a top speed of 25.2km/h?arrow_forwardA certain car traveling at 97 km/h can stop in 46 m on a level road. Determine the coefficient of friction between the tires and the road. Assume that the car starts skidding the moment the driver hits the brakes.arrow_forward
- A box weighing 1000 N is sitting in an inclined plane with an angle of 45°. Given the coefficient of friction of 0.25, calculate the horizontal force that can start the box the moving forward.arrow_forwardA force of 65N is needed to start an 8kg box moving across a horizontal surface. (A) Calculate the coefficient of static friction. (B) If the box continues to move with an acceleration of 1.4m/s². What is the coefficient of kinetic friction?arrow_forwardShoes made for the sports of boulderingand rock climbing are designed to provide a great deal of frictionbetween the foot and the surface of the ground. Such shoes on smoothrock might have a coefficient of static friction of 1.2 and a coefficient ofkinetic friction of 0.90. A person wearing these shoes stands on a smooth, horizontal rock. She pushes against the ground to begin running. What is the maximum horizontal acceleration she can have without slipping? (a) 0.20g; (b) 0.75g; (c) 0.90g; (d) 1.2g.arrow_forward
- The FedEx and UPS boxes have almost reached the top of the inclined plane they have been moving along and are now arrangedThe UPS box has a mass of 3.0 kg, and the FedEx box has a mass of 1.0 kg. The inclined plane is frictionless;however, the horizontal floor has coefficients of static and kinetic friction of 0.5 and 0.2. The pulley is frictionless, and the massesof the pulley and cord are negligible. Answer the following about this system. a.What is the size of the normal force on the UPS box?b. This system will begin to move if released from rest. However, if youpressed with a downward force on the FedEx box, this system could remain at rest.What size force is required? Your solution should include two free-body diagrams.c. If the system was set into motion down the ramp, without the forcementioned in the previous part, what would be the acceleration of the system? Yoursolution should include two free-body diagrams.arrow_forwardA coffee cup on the horizontal dashboard of a car slides forward when the driver decelerates from 45 km/h to rest in 3.5 s or less, but not if she decelerates in a longer time.What is the coefficient of static friction between the cup and the dash? Assume the road and the dashboard are level (horizontal).arrow_forwardA 6.7 kg mass is released from rets while on an incline of 53.96 degrees. If the coefficient of kinetic friction is 0.478 what is the magnitude of the acceleration of the mass?arrow_forward
- In a pickup game of dorm shuffleboard, students crazed by final exams use a broom to propel a calculus book along the dorm hallway. If the 3.5 kg book is pushed from rest through a distance of 0.92 m by the horizontal 26 N force from the broom and then has a speed of 1.28 m/s, what is the coefficient of kinetic friction between the book and floor?arrow_forwardSuppose the coefficient of static friction between a quarterand the back wall of a rocket car is 0.330. At what minimumrate would the car have to accelerate so that a quarter placedon the back wall would remain in place?arrow_forwardA mover is pushing a 148kg box up a ramp. The ramp is inclined at an angle of 30.4 degrees. Since the box is on wheels, assume that friction is negligable. Calculate the force the mover exerts to push the box up the ramp at a constant rate of 1.26 m/s. Assume he pushes parallel to the ramp.arrow_forward
- University Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice University