Chapter 8: Force – Step-by-Step Physics Study Guidance

Q1. A car merges onto a freeway, accelerating from 60 km/h to 80 km/h. As it does this, a bus passes by in the fast lane, travelling at a constant 100 km/h. Which vehicle has the greater magnitude of the vector sum of forces acting on it?

Background

Topic: Newton's Second Law and Forces

This question tests your understanding of how the net force (vector sum of forces) relates to acceleration, and how to compare forces acting on objects moving at different velocities and accelerations.

Key Terms and Formulas

• Newton's Second Law: $\vec{F}_{\text{net}} = m \vec{a}$

• Acceleration ($a$): The rate of change of velocity.

• Constant velocity: $a = 0$, so $\vec{F}_{\text{net}} = 0$.

Step-by-Step Guidance

1. Identify which vehicle is accelerating and which is moving at constant velocity.

2. Recall that a nonzero net force is required for acceleration, while constant velocity means zero net force.

3. Apply Newton's Second Law to each vehicle: $\vec{F}_{\text{net}} = m \vec{a}$.

4. Compare the net forces based on the acceleration of each vehicle.

Try solving on your own before revealing the answer!

Q2. You wish to move a crate. (a) Is there a minimum value for the magnitude of the pushing force you have to exert to set the crate in motion? (b) Is there a minimum value for the magnitude of the vector sum of forces that must be exerted on the crate to set it in motion?

Background

Topic: Static Friction and Net Force

This question explores the concept of static friction and the conditions required to initiate motion in an object at rest.

Key Terms and Formulas

• Static friction force: $f_{s,\text{max}} = \mu_s N$

• Net force: $\vec{F}_{\text{net}} = m \vec{a}$

• Normal force ($N$): For a horizontal surface, $N = mg$

Step-by-Step Guidance

1. Consider the forces acting on the crate: applied force, friction, and normal force.

2. Recall that to start moving the crate, the applied force must overcome the maximum static friction.

3. Set up the inequality: $F_{\text{push}} > f_{s,\text{max}}$.

4. Think about what the net force is at the instant the crate just starts to move.

Try solving on your own before revealing the answer!

Q4. The x component of the vector sum of forces exerted on a cart moving on a low-friction track is measured in the laboratory with the aid of a spring-loaded sensor and a monitoring computer. From the data in the table, sketch the $F_x(t)$ curve of the cart and use your graph to estimate the change in the cart’s momentum.

Background

Topic: Impulse and Change in Momentum

This question tests your ability to interpret force vs. time data, sketch the corresponding curve, and relate the area under the curve to the change in momentum (impulse).

Key Terms and Formulas

• Impulse: $J = \Delta p = \int_{t_i}^{t_f} F_x(t) dt$

• For discrete data, the area under the $F_x$ vs. $t$ curve can be estimated using geometric shapes or numerical methods.

Step-by-Step Guidance

1. Plot the given $F_x$ values against time to sketch the $F_x(t)$ curve.

2. Identify the shape(s) formed under the curve (e.g., rectangles, triangles, trapezoids).

3. Estimate the area under the curve, which represents the impulse delivered to the cart.

4. Recall that impulse equals the change in momentum: $\Delta p = J$.

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Q10. During a tennis volley, a ball that arrives at a player at 40 m/s is struck by the racquet and returned at 40 m/s. The other player, realizing that the ball is out of bounds, catches it in her hand. Assuming the time interval of contact is the same in both cases, compare the force exerted by the first player’s racquet on the ball with the force exerted by the second player’s hand on the ball.

Background

Topic: Impulse and Force During Collisions

This question examines how the change in momentum (impulse) and contact time affect the average force exerted during different types of collisions.

Key Terms and Formulas

• Impulse: $J = \Delta p = F_{\text{avg}} \Delta t$

• Change in momentum: $\Delta p = m(v_f - v_i)$

• Contact time ($\Delta t$): The duration of force application.

Step-by-Step Guidance

1. Calculate the change in velocity for the ball in each scenario (racquet hit vs. catch).

2. Determine the change in momentum ($\Delta p$) for each case.

3. Recall that the average force is $F_{\text{avg}} = \frac{\Delta p}{\Delta t}$.

4. Compare the magnitudes of $\Delta p$ and thus $F_{\text{avg}}$ for both cases, given the same contact time.

Try solving on your own before revealing the answer!