A car moves in a circle of radius 40m with a constant speed of 16m/s. The radial force will be:a.25700Nb.25600Nc.24500Nd.23500N

1. Break Down the Problem

To find the radial (centripetal) force acting on the car moving in a circular path, we need to use the formula for centripetal force: $F_c = \frac{mv^2}{r}$ where:

• $F_c$ = centripetal force (N)
• $m$ = mass of the car (kg)
• $v$ = speed of the car (m/s)
• $r$ = radius of the circular path (m)

However, we are not given the mass of the car, so we need its value to compute the force. We'll just highlight the necessary steps.

2. Relevant Concepts

1. Identify centripetal acceleration: $a_c = \frac{v^2}{r}$
2. Calculate the force using the mass $m$: $F_c = m \cdot a_c$

3. Analysis and Detail

1. Compute the centripetal acceleration: $a_c = \frac{(16\, \text{m/s})^2}{40\, \text{m}} = \frac{256}{40} = 6.4\, \text{m/s}^2$
2. The formula for force requires the mass $m$. Without this information, we can represent the centripetal force as: $F_c = m \cdot 6.4\, \text{N}$

4. Verify and Summarize

Since the mass of the car is unknown, we cannot provide a numeric answer based on the options given (25700N, 25600N, 24500N, 23500N) without that value.

Given that $F_c$ would depend on the value of $m$, you can substitute the mass of the car into $F_c = m \cdot 6.4\, \text{N}$ to find the specific force.

Final Answer

In summary, we need the mass of the car to calculate the exact radial force. If the mass of the car is provided, we can then compute the centripetal force.