(1562.5 J]
3. A 3 kg mass starts at rest at the top of 37° incline which is 5 m long. Its speed as it reaches
the bottom is 2 ms. Use energy method to find the average frictional force which
retarded its motion.
Answers
Answer
hope it helps uu...
frnd,...
Hence the average frictional force which retarded the motion of the mass is equal to 16.8 Newton.
Given:
Mass of the given object (m) = 3 kg
The angle of inclination of the inclined plane (θ) = 37°
Length of the inclined plane (L) = 5m
Speed of the mass on reaching the bottom (v) = 2 ms⁻¹
To Find:
The average frictional force which retarded the motion of the mass.
Solution:
→ As the length of the inclined plane (L) is equal to 5 m and the angle of inclination of the inclined plane (θ) is 37° therefore the vertical height (H) of the highest point of the inclined plane will be equal to Lsin37°.
∴ H = Lsin37° = 5 (3/5) = 3 m
→ According to the Law of conservation of energy for an isolated system the total energy of a system remains conserved, it only changes its form from one form to another.
→ But in the presence of a frictional force, the mechanical energy which is the sum of potential energy (U) and kinetic energy (K) does not remains conserved. The final mechanical energy which is the sum of potential energy and kinetic energy will be less than the initial mechanical energy. This is because some energy is lost in doing work against the friction.
→ Potential energy of the mass at a height of 3 m (U₁) = mgH = 3 × 10 × 3
∴ U₁ = 90 J
→ The kinetic energy of the mass at a height of 3 m (K₁) = 0 (mass is at rest)
→ The potential energy of the mass at the bottom (U₂) = 0
→ The kinetic energy of the mass at the bottom (K₂) = 1/2(mv²) = 1/2(3×2²)
∴ K₂ = 6 J
→ Initial mechanical energy (E₁) = U₁ + K₁ = 90 + 0 = 90 J
→ Final mechanical energy (E₂) = U₂ + K₂ = 0 + 6 = 6 J
∴ The mechanical energy lost due to friction (ΔE) = E₁ - E₂ = 90 - 6 = 84 J
→ As we know that friction acts in a direction opposite to the direction of motion. Hence if the frictional force is 'F' and the displacement is 'S' then the formula for the work done (W) against the friction is given as:
∴ W = FS cosθ = FS cos(180°) = -FS
∴ W = -(FS)
→ The negative sign of the work indicates that the work done by the friction is in a direction opposite to the direction of motion.
→ The length of the inclined plane is 5 m. Therefore the displacement (S) against the frictional force will be equal to 5 m.
→ The work done by the frictional force will be equal to loss in the total mechanical energy of the mass.
∴ W = ΔE = 84 J
∴ W = FS = 84
∴ F (5) = 84
∴ F = 16.8 N
Hence the average frictional force which retarded the motion of the mass is equal to 16.8 Newton.
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