5.7 Drawing Free-Body Diagrams

If a book is located on a table, how many forces should be shown in a free-body diagram of the book? Describe them.

Two forces of 25 and 45 N act on an object. Their directions differ by $70 °$. The resulting acceleration has magnitude of $10.0 \text{m}/\text{s}^{2} .$ What is the mass of the body?

(a) Find an equation to determine the magnitude of the net force required to stop a car of mass m, given that the initial speed of the car is $v_{0}$ and the stopping distance is x. (b) Find the magnitude of the net force if the mass of the car is 1050 kg, the initial speed is 40.0 km/h, and the stopping distance is 25.0 m.

A force acts on a car of mass m so that the speed v of the car increases with position x as $v = k x^{2}$, where k is constant and all quantities are in SI units. Find the force acting on the car as a function of position.

Two boxes, A and B, are at rest. Box A is on level ground, while box B rests on an inclined plane tilted at angle $\theta$ with the horizontal. (a) Write expressions for the normal force acting on each block. (b) Compare the two forces; that is, tell which one is larger or whether they are equal in magnitude. (c) If the angle of incline is $10 °$, which force is greater?

In building a house, carpenters use nails from a large box. The box is suspended from a spring twice during the day to measure the usage of nails. At the beginning of the day, the spring stretches 50 cm. At the end of the day, the spring stretches 30 cm. What fraction or percentage of the nails have been used?

Two forces are applied to a 5.0-kg object, and it accelerates at a rate of $2.0 \text{m}/\text{s}^{2}$ in the positive y-direction. If one of the forces acts in the positive x-direction with magnitude 12.0 N, find the magnitude of the other force.

On June 25, 1983, shot-putter Udo Beyer of East Germany threw the 7.26-kg shot 22.22 m, which at that time was a world record. (a) If the shot was released at a height of 2.20 m with a projection angle of $45.0 °$, what was its initial velocity? (b) If while in Beyer’s hand the shot was accelerated uniformly over a distance of 1.20 m, what was the net force on it?

A body of mass m has initial velocity $v_{0}$ in the positive x-direction. It is acted on by a constant force F for time t until the velocity becomes zero; the force continues to act on the body until its velocity becomes $− v_{0}$ in the same amount of time. Write an expression for the total distance the body travels in terms of the variables indicated.

A 120-kg astronaut is riding in a rocket sled that is sliding along an inclined plane. The sled has a horizontal component of acceleration of $5.0 \text{m} / \text{s}^{2}$ and a downward component of $3.8 \text{m} / \text{s}^{2}$. Calculate the magnitude of the force on the rider by the sled. (Hint: Remember that gravitational acceleration must be considered.)

Suppose that you are viewing a soccer game from a helicopter above the playing field. Two soccer players simultaneously kick a stationary soccer ball on the flat field; the soccer ball has mass 0.420 kg. The first player kicks with force 162 N at $9.0 °$ north of west. At the same instant, the second player kicks with force 215 N at $15 °$ east of south. Find the acceleration of the ball in $\hat{i}$ and $\hat{j}$ form.

A 0.0502-kg pair of fuzzy dice is attached to the rearview mirror of a car by a short string. The car accelerates at constant rate, and the dice hang at an angle of $3.20 °$ from the vertical because of the car’s acceleration. What is the magnitude of the acceleration of the car?

An object is acted on by three simultaneous forces: $\overset{\rightarrow}{F}_{1} = \left(−3.00 \hat{i} + 2.00 \hat{j}\right) \text{N}$, $\overset{\rightarrow}{F}_{2} = \left(6.00 \hat{i} - 4.00 \hat{j}\right) \text{N}$, and $\overset{\rightarrow}{F}_{3} = \left(2.00 \hat{i} + 5.00 \hat{j}\right) \text{N}$. The object experiences acceleration of $4.23 \text{m}/\text{s}^{2}$. (a) Find the acceleration vector in terms of m. (b) Find the mass of the object. (c) If the object begins from rest, find its speed after 5.00 s. (d) Find the components of the velocity of the object after 5.00 s.

A drone is being directed across a frictionless ice-covered lake. The mass of the drone is 1.50 kg, and its velocity is $3.00 \hat{i} \text{m} / \text{s}$. After 10.0 s, the velocity is $9.00 \hat{i} + 4.00 \hat{j} \text{m} / \text{s}$. If a constant force in the horizontal direction is causing this change in motion, find (a) the components of the force and (b) the magnitude of the force.