Final answer:
The acceleration of a 1.95 kg block on a rough patch with a coefficient of friction of 0.26 is approximately 2.5617 m/s² in the opposite direction to its motion. This calculation was derived using force and motion equations considering the force of friction opposing the block's initial velocity.
Step-by-step explanation:
To find the acceleration of the block when it is on the rough patch, we need to use the formula F = ma, where F is the force acting on the block, m is the mass of the block, and a is the acceleration. The only horizontal force acting on the block while it is on the rough patch is the frictional force, which can be calculated using Ffriction = μN, where μ is the coefficient of friction and N is the normal force. In this case, the normal force is equal to the weight of the block since the surface is horizontal, so N = mg. The frictional force opposing the motion of the block is therefore Ffriction = μ mg.
Given that the mass m = 1.95 kg, the initial speed is not necessary for calculating the acceleration due to friction. The coefficient of friction μ = 0.26, and the acceleration due to gravity g = 9.81 m/s2, the frictional force is:
• Ffriction = (0.26)(1.95 kg)(9.81 m/s2)
• Ffriction = 4.9983 N (approximately)
Now, using F = ma, we isolate a:
• a = Ffriction/m
• a = 4.9983 N / 1.95 kg
• a = 2.5617 m/s2 (approximately)
Thus, the acceleration of the block on the rough patch is about 2.5617 m/s2 in the opposite direction of motion. The negative sign indicates deceleration.