To analyze the motion of the crate, we must first consider the forces exerted on it and apply Newton's second law of motion.
You are applying a force of 10 N to the right, while your friend is applying a force of 25 N to the left. To find the net force acting on the crate, we need to subtract the force you apply from the force your friend applies:
\[ \text{Net Force} = \text{Force by your friend} - \text{Your force} = 25 , \text{N (left)} - 10 , \text{N (right)} = 15 , \text{N (left)} \]
This calculation indicates that the net force on the crate is 15 N to the left, meaning that the leftward force is greater than the rightward force.
According to Newton's second law (F = ma), the motion of an object is determined by the net force acting on it:
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Direction of Motion: Since the net force is directed to the left, the crate will accelerate to the left.
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Acceleration: The actual acceleration of the crate can be calculated if we know its mass. For example, if the mass of the crate is \( m \), the acceleration \( a \) can be calculated using the net force:
\[ a = \frac{F_{net}}{m} = \frac{15 , \text{N}}{m} \]
Thus, the crate will move to the left with an acceleration proportional to the net force divided by its mass.
Summary: The crate experiences a net force of 15 N to the left and will accelerate to the left. The success of this leftward movement will depend on the mass of the crate, but the dominant force to the left guarantees that it will indeed move in that direction.