9. A toy cart at the end of a string 0.70 m long moves in a circle on a table. The cart has a mass of 2 kg and the string has a breaking strength of 40 N. Calculate the maximum speed the cart can attain without breaking the string? ( \( 3.74 \mathrm{~m} / \mathrm{s}) \)

Un cilindro graduato contiene inizialmente un volume d'acqua pari a \( (200 \pm 5) \mathrm{cm}^{3} \). Un oggetto viene immers completamente in acqua e il volume dell'acqua sale \( (345 \pm 5) \mathrm{cm}^{3} \). Calcola il volume dell'oggetto.

To monitor the breathing of a hospital patient, a thin belt is girded around the patient's chest. The belt is a 200-turn coil. When the patient inhales, the area encircled by the coil increases by \( 45.0 \mathrm{~cm}^{2} \). The magnitude of the Earth's magnetic field is \( 50.0 \mu \mathrm{~T} \) and makes an angle of \( 28.0^{\circ} \) with the plane of the coil. Assuming a patient takes 1.89 s to inhale, find the average induced emf in the coil during this time interval. 21.02

aceleración es el cambio de velocidad respecto al cambio de tiempo, esto es: \( =\frac{\Delta v}{\Delta t}=\frac{v-v_{0}}{t-t_{0}} \) Como \( v_{0} \) es la velocidad inicial, en nuestro caso es cero por estar en repos nbién \( t_{0} \) representa el tiempo inicial el cual es de 0 segundos. Por lo anterior la aceleració \( =\frac{v}{t} \quad v=a t \) el caso anterior vimos que la distancia se determina con la fórmula. stancia \( =\int_{a}^{b} v d t \quad \) como \( v=a t \) stancia \( =\int_{0}^{8} a t d t \) pero \( a=\frac{40 \frac{m}{s}}{8 s}=5 \frac{m}{s^{2}} \) entonces distancia \( =\int_{0}^{8} 5 \frac{m}{s^{2}} t d t \) suelve la integral y encuentra la distancia recorrida en ese intervalo de tiempo. Ialmente, en la gráfica comprueba que la distancia recorrida representa el área bajo la rec ea= (base)(altura)/2.

Find the current through section \( P Q \) of length \( a=62.0 \mathrm{~cm} \) shown in Figure P31.11. The circuit is located in a magnetic field whose magnitude varies with time according to the expression \( B=\left(1.00 \times 10^{-3} \mathrm{~T} / \mathrm{s}\right) t \). Assume the resistance per length of the wire is \( 0.098 \Omega / \mathrm{m} \). Magnitude

2. STEM Density is measured in units of mass per unit of volume. It can be thought of as a unit rate. The mass of a block of aluminum is 9.45 grams. The volume is 3.5 cubic centimeters \( \left(\mathrm{cm}^{3}\right) \). What is the density of the aluminum?