A 3.0 kg particle is moving with a velocity v(t) = (5.0î + 7.0tĵ) m/s?
(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)
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
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.
收錄日期: 2021-04-24 01:02:50
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