A block of weight 41.8 N is hanging from a rope. The tension in the rope is 24.4 N, pulling upward on the block. What is the magnitude and direction of the acceleration of the block?
I know the direction would be downwards, since the tension of the rope is less than the weight of the block. I'm more so confused about the magnitude. Please help!
Thank you
To determine the magnitude and direction of the acceleration of the block, you can use Newton's second law of motion. This law states that the net force acting on an object is equal to the product of its mass and acceleration:
Fnet = ma
In this case, the net force is the difference between the tension in the rope and the weight of the block:
Fnet = tension - weight
Substituting the given values:
Fnet = 24.4 N - 41.8 N
Fnet = -17.4 N
The negative sign indicates that the net force is directed downward, which aligns with our understanding that the tension is less than the weight of the block.
To calculate the acceleration, we can rearrange the equation:
a = Fnet / m
Since the mass of the block is not provided, we need to find a way to compute it. We can use Newton's second law again:
Fnet = ma
Rearranging the equation:
m = Fnet / a
Substituting the given values:
m = -17.4 N / a
The mass will cancel out when dividing the tension by the mass:
41.8 N / a = 24.4 N
Next, we can solve for acceleration:
a = 41.8 N / 24.4 N
a ≈ 1.71 m/s²
Therefore, the magnitude of the acceleration is approximately 1.71 m/s², and the direction is downwards.