Answer:
(a) the coefficient of friction is 0.451
This was derived using the energy conservation principle (the total energy in a closed system remains constant).
(b) No, the object stops 5.35 m away from point B. This is due to the spring's expansion only performing 43 J of work on the block, which isn't sufficient compared to the 398 J required to overcome friction.
Explanation:
For more details on how this issue was resolved, refer to the attached material. The solution for part (a) separates the body’s movement into two segments: from point A to B, and from B to C. The total system energy originates from the initial gravitational potential energy, which transforms into work against friction and into work compressing the spring. A work of 398 J is needed to counteract friction over the distance of 6.00 m. The energy used for this is lost since friction is not a conservative force, leaving only 43 J for spring compression. When the spring expands, it exerts a work of 43 J back on the block, which is only sufficient to move it through a distance of 0.65 m, stopping 5.35 m short of point B.
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Answer:
d) v1 = v2 = v3
Explanation:
This can be determined through the principle of energy conservation. We assess the total mechanical energy E=K+U (the sum of kinetic energy and gravitational potential energy) at both the initial and final positions, ensuring they remain constant.
<pInitially, for the three spheres, we have:Finally, for the three spheres, we see:
Response: The spring constant is 25 N/m.
Details:
The body’s mass is 25 g, which converts to 0.025 kg (since 1 kg = 1000 g).
The total oscillations are 20 in 4 seconds.
Oscillations per second =
Spring's frequency of vibration is =
The spring constant 'k' can be derived from the relationship involving frequency, mass, and spring constant.
The spring constant is 25 N/m.
The resultant force acting on the shopping cart is 12 N to the right.
This is a scenario related to Newton's Laws. A Free Body Diagram can be utilized to illustrate all the forces acting on the object. There are four forces at play:
The first two forces (1 and 2) counteract one another as they are equal, while the overall force can be determined by combining forces (3) and (4)
The positive value indicates that the shopping cart is moving towards the right.
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Answer:
A = 4.76 x 10⁻⁴ m²
Explanation:
Given data:
Person's weight = 625 N
Bike's weight = 98 N
Pressure per tire = 7.60 x 10⁵ Pa
Find: Contact area per tire
Total system weight = 625 + 98 = 723 N
Let F represent the force supported by each tire
2F = 723 N
Therefore, F = 361.5 N
Using the formula F = P × A
Contact area, A = 4.76 x 10⁻⁴ m²