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What force (in N) must be applied to a 500.0 kg crate on a frictionless plane inclined at 30° to cause an acceleration of 5.0 m/s^2 up the plane? (Enter the magnitude.)

Sagot :

onyebuchinnaji

The force must be applied to the crate on a frictionless plane to cause the acceleration is is 4,243.4 N

The given parameters;

  • mass of the crate, m = 500 kg
  • inclination of the angle, θ = 30⁰
  • acceleration of the crate, a = 5 m/s²

The force that must be applied to the crate to cause the acceleration is calculated as follows;

F = ma

∑Fₓ = 0

mgcosθ - F[tex]_k[/tex] = F

where;

  • F[tex]_k[/tex] is the frictional force on crate

mgcosθ - 0 = F

mgcosθ = F

500 x 9.8 x cos(30) = F

4,243.4 N

Thus, the force must be applied to the crate on a frictionless plane to cause the acceleration is is 4,243.4 N.

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