Concept explainers
A 1 000-kg car is pulling a 300-kg trailer. Together, the car and trailer move forward with an acceleration of 2.15 m/s2. Ignore any force of air drag on the car and all frictional forces on the trailer. Determine (a) the net force on the car, (b) the net force on the trailer, (c) the force exerted by the trailer on the car, and (d) the resultant force exerted by the car on the road.
(a)
The net force on the car.
Answer to Problem 42P
The net force on the car is
Explanation of Solution
The free body diagram for the system is given by figure 1.
Write the expression for the net force along horizontal direction.
Here,
The car is having only horizontal acceleration.
Conclusion:
Substitute,
The net force is acting along forward direction.
Thus, the net force on the car is
(b)
The net force on the trailer.
Answer to Problem 42P
The net force on the car is
Explanation of Solution
Write the expression for the net force along horizontal direction.
Here,
Conclusion:
Substitute,
The net force is acting along forward direction.
Thus, the net force on the car is
(c)
The force exerted by the trailer on the car.
Answer to Problem 42P
The force exerted by the trailer on the car is
Explanation of Solution
According to the Newton’s third each and every action has equalled and opposite reaction. In the given problem, the force acting on the trailer given by the car is 645N. This force is directed along forward.
Thus, according to Newton’s third law, the trailer will also give same amount of force on the car. Hence, The force exerted by the trailer on the car is
(d)
The resultant force exerted by the car on the road.
Answer to Problem 42P
The resultant force exerted by the car on the road is
Explanation of Solution
Write the expression for the net force exerted by the road acting on the car.
Here,
Write the expression for the x-component of force.
Write the expression for the y-component of force.
Here,
Write the expression for the magnitude of the net force exerted by the road on the car by using (IV) and (V).
Here,
Write the expression for the magnitude of the net force exerted by the road on the car by using (IV) and (V).
Here,
Conclusion:
Substitute,
Substitute,
Here, the force with magnitude
Thus, according to Newton’s third law, the resultant force exerted by the car on the road is
Want to see more full solutions like this?
Chapter 4 Solutions
Principles of Physics: A Calculus-Based Text
- If a single constant force acts on an object that moves on a straight line, the objects velocity is a linear function of time. The equation v = vi + at gives its velocity v as a function of time, where a is its constant acceleration. What if velocity is instead a linear function of position? Assume that as a particular object moves through a resistive medium, its speed decreases as described by the equation v = vi kx, where k is a constant coefficient and x is the position of the object. Find the law describing the total force acting on this object.arrow_forwardA force F applied to an object of mass m1 produces an acceleration of 3.00 m/s2. The same force applied to a second object of mass m2 produces an acceleration of 1.00 m/s2. (a) What is the value of the ratio m1/m2? (b) If m1 and m2 are combined into one object, find its acceleration under the action of the force F.arrow_forwardA crate is sitting on a horizontal surface where the coefficient of static friction is 0.60. A worker pushes horizontally on the crate, which has a mass of 45 kg. The crate does not move, and there are no other forces acting on it. Which of the following statements is true? (a) The force of friction on the crate is mgμs. (b) The force of friction on the crate is mgμk. (c) The force of friction on the crate is greater than the force that the worker exerts on the crate. (d) The force exerted on the worker by the crate is equal in magnitude to the force of friction exerted by the surface on the crate.arrow_forward
- A 2.5 kg block is initially at rest on a horizontal surface. A horizontal force F of magnitude 6.2 N and a vertical force P are then applied to the block. The coefficients of friction for the block and surface are us = 0.38 and uk = 0.22. (a) Determine the magnitude of the frictional force acting on the block if the magnitude of P is 8.0 N. (b) Determine the magnitude of the frictional force acting on the block if the magnitude of P is 10.0 N. (c) Determine the magnitude of the frictional force acting on the block if the magnitude of P is 12.0 N.arrow_forwardA 620 kg car pulling a 495 kg trailer accelerates forward at a rate of 2.20 m/s2. Assume frictional forces on the trailer are negligible. Ignore air drag. (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 (in N): Direction: (measured from the left of the −y-direction in degrees)arrow_forwardA 1030 kg car is pulling a 280 kg trailer. Together, the car and trailer have an acceleration of 2.00 m/s2 in the forward direction. Neglecting frictional forces on the trailer, determine the following (including sign).(b) the net force on the trailer (c) the force exerted by the trailer on the car (d) the resultant force exerted by the car on the roadarrow_forward
- The acceleration of an object has a magnitude a. What is the magnitude of the acceleration in the following cases? (a) All the forces acting on the object are doubled.(b) The mass and the net force acting on the object are doubled. (c) The net forceacting on the object is doubled, and its mass is halved. (d) The mass of the object isdoubled, and the net force acting on it is halved.arrow_forwardLon Mauer is cleaning up the driveway after mowing the grass. He exerts a sudden downward force of 56.8 N at a constant angle of 54.7° directed below the horizontal direction in order to push and accelerate his 1.05-kg broom from rest. The rate of acceleration of the broom is 0.670 m/s/s. Determine the coefficient of friction between the broom bristles and the driveway.arrow_forwardA plate of cafeteria food is on a horizontal table. You push it away from you with a constant horizontal force of 14.0 N. The plate has a mass of 0.800 kg, and during the push it has an acceleration of 12.0 m/s2 in the direction you are pushing it. (a) What is the magnitude of the net external force on the plate during the push? (b) What are the magnitude and direction of the friction force that the table exerts on the plate during the push?arrow_forward
- A 2.5 kg block is initially at rest on a horizontal surface. A horizontal force F of magnitude 6.2 N and a vertical force P are then applied to the block. The coefficients of friction for the block and surface are ls = 0.37 and Uk = 0.22. (a) Determine the magnitude of the frictional force acting on the block if the magnitude of P is 8. N. (b) Determine the magnitude of the frictional force acting on the block if the magnitude of P is 10.0 N. N (c) Determine the magnitude of the frictional force acting on the block if the magnitude of P is 12.0 N. N Submit Answerarrow_forwardA man has to push his boat on the shore across the mud to get to the water. The coefficient of friction between the boat and the mud is given by μ = 0.400. If the boat has a mass of 40 kg, calculate the magnitude of the force of friction acting on the boat.arrow_forwardTwo forces FA and FB are applied to an object whose mass is 19.9 kg. The larger force is FA. When both forces point due east, the object's acceleration has a magnitude of 0.687 m/s2. However, when FA points due east and FB points due west, the acceleration is 0.510 m/s², due east. Find (a) the magnitude of FÅ and (b) the magnitude of FB (a) Number i (b) Number i Units Units îarrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning