A 3.0 kg particle is moving with a velocity v(t) = (5.0î + 7.0tĵ) m/s?

2018-04-13 1:25 pm
(Assume momentum is in kg · m/s, force is in newtons, and t is in seconds. Express your answers in vector form. Use the following as necessary: t.

The momentum (as a function of time) of this particle;

p(t) 15i + 21tj kg*m/s

What is the net force acting on this particle?

F(t) = ?

回答 (2)

2018-04-13 1:41 pm
From time = t₁ to time = t₂ :
Change in momentum, Δp(t) = (15i + 21t₂j) - (15i + 21t₁j) = 21(t₂ - t₁)j kg•m/s
Time taken, t = (t₂ - t₁) s

Force = ma = m(Δv/t) = mΔv/t = Δp(t)/t = 21(t₂ - t₁)j/(t₂ - t₁) kg•m/s² = 21j N
2018-04-13 1:42 pm
The most general expression of Newton's second law is that the net force on an object is equal to the derivative of the object's momentum with respect to time: F = dp/dt, where F is the net force and p is the momentum. Both F and p are vector quantities, and both could be dependent on time. When the object has a constant mass, then F = m*dv/dt = m*a, which is what most beginning physics students recognize as the second law.

Here, we are told that m = 3.0 kg (constant mass) and v(t) = (5.0*î + 7.0*t*ĵ) m/s, so p(t) = m*v(t) = (15.0*î + 21.0*t*ĵ) kg*m/s

F = dp(t)/dt = (0*i + 21.0*j) kg*m/s² = (0*i + 21.0*j) N

The net force on the object is a constant force of 21.0 N in the positive y direction.


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