搜狗做题网A ball of mass m is attached to a string of length L.It is s
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A ball of mass m is attached to a string of length L.It is swung in a vertical circle with enough speed to keep the string taut throughout the motion.Assume the ball travels freely in the circle with negligible loss of mechanical energy.Determine if the following six statements are true or false; e.g.,enter TTFFFF.
mvt2/L = Tt−mg,where vt and Tt are the speed of the ball and the tension of the string at the top of the circle.
The speed of the ball at the bottom of the circle is greater than the speed at the top of the circle.
The tension in the string is less at the top of the circle than at the bottom of the circle.
The difference between the tensions at the top and at the bottom of the circle is independent of the speed of the ball.
The acceleration of the ball at the top of the circle is directed `up'.
The tension in the string at the top of the circle is always greater than the weight of the ball.
Assume that m = 0.31 kg and L = 1.23 m.What is the difference in tension,Tb−Tt,between when the ball is at the bottom and when it is at the top?
mvt2/L = Tt−mg,where vt and Tt are the speed of the ball and the tension of the string at the top of the circle.
The speed of the ball at the bottom of the circle is greater than the speed at the top of the circle.
The tension in the string is less at the top of the circle than at the bottom of the circle.
The difference between the tensions at the top and at the bottom of the circle is independent of the speed of the ball.
The acceleration of the ball at the top of the circle is directed `up'.
The tension in the string at the top of the circle is always greater than the weight of the ball.
Assume that m = 0.31 kg and L = 1.23 m.What is the difference in tension,Tb−Tt,between when the ball is at the bottom and when it is at the top?
英文的大致意思是：用一根长为L的绳连着一个质量为m的球,让它在竖直平面内做自由圆周运动,（最高点也可以通过）问下面六个哪些正确（T),哪些错误（F)
1.F（Tt和Vt分别为最高点的绳的拉力和速度.mvt2/L = Tt+mvt2/L = Tt−mg）
2,T（在圆周最底部的速度自然大于最高点的速度,因为除了重力之外没有任何力作用于这个绳和球构成的系统,由最高点到最低点重力势能转化为动能,故动能增大）
3.T（最高点T=mvt2/L -mg,最低点Tb=mv2/L +mg,v>vt)
4.F,（最高点T=mvt2/L -mg,最低点Tb=mv2/L +mg,v>vt)
5.F（加速度方向指向圆心,故应该向下）
6..F（最高点的T=mvt2/L -mg,故没法和重力比较大小
最高点mVt2=Tt+mg
最低点mV2=Tb-mg
mg*2L=0.5mV2-0.5mVt2
联合上面三式求解得
Tb-Tt=4mgL-2mg=4*0.31*10*1.23-2*0.31*10=5.95N
1.F（Tt和Vt分别为最高点的绳的拉力和速度.mvt2/L = Tt+mvt2/L = Tt−mg）
2,T（在圆周最底部的速度自然大于最高点的速度,因为除了重力之外没有任何力作用于这个绳和球构成的系统,由最高点到最低点重力势能转化为动能,故动能增大）
3.T（最高点T=mvt2/L -mg,最低点Tb=mv2/L +mg,v>vt)
4.F,（最高点T=mvt2/L -mg,最低点Tb=mv2/L +mg,v>vt)
5.F（加速度方向指向圆心,故应该向下）
6..F（最高点的T=mvt2/L -mg,故没法和重力比较大小
最高点mVt2=Tt+mg
最低点mV2=Tb-mg
mg*2L=0.5mV2-0.5mVt2
联合上面三式求解得
Tb-Tt=4mgL-2mg=4*0.31*10*1.23-2*0.31*10=5.95N
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