Question

(score for question 1: ___ of 5 points)

1. when you lift a book from the ground to your desk, what kind of work do you do, negative or positive? by lifting the book, what do you change? does the book gain or lose energy? what kind of energy?

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(score for question 2: ___ of 5 points)

1. a ball with a mass of 5.0 g is moving at a speed of 2.0 m/s. would doubling the mass or doubling the speed have a greater effect on the kinetic energy of the ball? explain.

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Explanation:

Question 1

To determine the work done, we use the work formula \( W = Fd\cos\theta \). When lifting the book, the force (your upward force) and displacement (upward) are in the same direction, so \( \theta = 0^\circ \) and \( \cos\theta = 1 \), resulting in positive work. Lifting the book changes its height, which changes its gravitational potential energy (since \( PE_g = mgh \), and \( h \) increases). The book gains energy, specifically gravitational potential energy.

Step 1: Recall the kinetic energy formula

The formula for kinetic energy is \( KE=\frac{1}{2}mv^{2} \), where \( m \) is the mass of the object and \( v \) is its speed.

Step 2: Analyze the effect of doubling the mass

Let the initial mass be \( m_1 = m \) and the initial speed be \( v_1 = v \). The initial kinetic energy \( KE_1=\frac{1}{2}mv^{2} \). If we double the mass, the new mass \( m_2 = 2m \) and the speed remains \( v_2=v \). The new kinetic energy \( KE_2=\frac{1}{2}(2m)v^{2}=mv^{2} \). To find the ratio of the new kinetic energy to the old one, we calculate \( \frac{KE_2}{KE_1}=\frac{mv^{2}}{\frac{1}{2}mv^{2}} = 2 \). So, doubling the mass doubles the kinetic energy.

Step 3: Analyze the effect of doubling the speed

If we double the speed, the new speed \( v_3 = 2v \) and the mass remains \( m_3=m \). The new kinetic energy \( KE_3=\frac{1}{2}m(2v)^{2}=\frac{1}{2}m\times4v^{2} = 2mv^{2} \). The ratio of the new kinetic energy to the old one is \( \frac{KE_3}{KE_1}=\frac{2mv^{2}}{\frac{1}{2}mv^{2}}=4 \). So, doubling the speed quadruples the kinetic energy.

Step 4: Compare the two effects

Since doubling the speed results in a four - fold increase in kinetic energy and doubling the mass results in a two - fold increase in kinetic energy, doubling the speed has a greater effect on the kinetic energy of the ball.

Answer:

When lifting the book, you do positive work. By lifting the book, you change its height (or position). The book gains energy, and the type of energy it gains is gravitational potential energy.

Question 2