A block-and-tackle system is used to lift a load of 20 N through a vertical height of 10 m. if the efficiency of the system is 40%, how much work is done against friction?
This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Let's calculate the work done against friction.
Step 1: Calculate the useful work done (Work output).
The useful work done is the work done on the load.
$$W_{\text{out}} = \text{Load} \times \text{Vertical height}$$
$$W_{\text{out}} = 20 \text{ N} \times 10 \text{ m}$$
$$W_{\text{out}} = 200 \text{ J}$$
Step 2: Use the efficiency to find the total work input.
Efficiency ($\eta$) is given by:
$$\eta = \frac{W_{\text{out}}}{W_{\text{in}}} \times 100\%$$
Given $\eta = 40\%$, we can rearrange to find $W_{\text{in}}$:
$$W_{\text{in}} = \frac{W_{\text{out}}}{\eta}$$
$$W_{\text{in}} = \frac{200 \text{ J}}{0.40}$$
$$W_{\text{in}} = 500 \text{ J}$$
Step 3: Calculate the work done against friction.
The work done against friction is the difference between the total work input and the useful work output.
$$W_{\text{friction}} = W_{\text{in}} - W_{\text{out}}$$
$$W_{\text{friction}} = 500 \text{ J} - 200 \text{ J}$$
$$W_{\text{friction}} = 300 \text{ J}$$
The work done against friction is $\boxed{\text{300 J}}$.
