Why did the block go to the spring for advice? Because it needed a little spring-tervention!
To find the work done by the spring, we can use the equation for work done by a spring, which is given by:
W = (1/2)kx²
where W is the work done, k is the spring constant, and x is the distance the spring is compressed.
Plugging in the values, we have:
W = (1/2)(295 N/m)(0.035 m)²
Simplifying this equation, we get:
W = 0.18 J
So, the work done by the spring in bringing the block to rest is 0.18 Joules.
Now, let's talk about the mechanical energy being dissipated by the force of friction. Well, it's quite a friction-al topic! The mechanical energy being dissipated by the force of friction can be found by calculating the work done by friction. The work done by friction is given by:
W = μkNΔx
where W is the work done by friction, μk is the coefficient of kinetic friction, N is the normal force, and Δx is the distance.
Since the normal force is equal to the weight of the block, which is mg, where m is the mass of the block and g is the acceleration due to gravity, we have:
N = mg = (1.60 kg)(9.8 m/s²)
Substituting the values, we get:
W = (0.5)(1.60 kg)(9.8 m/s²)(0.035 m)
Simplifying this equation, we find:
W = 0.27 J
So, the mechanical energy being dissipated by the force of friction is 0.27 Joules. Looks like some energy really rubbed off there!
To find the speed of the block when it hits the spring, we can use the concept of conservation of mechanical energy. At the starting point, the block has only kinetic energy, and at the compressed position, it has only potential energy stored in the spring. Assuming no other external forces, we have:
(1/2)mv² = (1/2)kx²
Where v is the velocity of the block.
Rearranging the equation, we get:
v = sqrt((k/m)x²)
Plugging in the given values, we have:
v = sqrt((295 N/m) / (1.60 kg)) * (0.035 m)
Calculating this equation, we find:
v ≈ 0.34 m/s
So, the speed of the block when it hits the spring is approximately 0.34 meters per second. It's springtime for the block!